Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations (1).pdf

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1、UncertaintyAnalysisbyDimensionReductionIntegrationandSaddlepointApproximationsBeiqingHuangPh.D.CandidateUncertaintyanalysis,whichassessestheimpactoftheuncertaintyofinputvariablesonGraduateResearchAssistantDepartmentofMechanicalandAerospaceresponses,isanindispens

2、ablecomponentinengineeringdesignunderuncertainty,suchEngineering,asreliability-baseddesignandrobustdesign.However,uncertaintyanalysisisanunaf-UniversityofMissouri–Rollafordablecomputationalburdeninmanyengineeringproblems.Inthispaper,anuncer-taintyanalysismethodi

3、sproposedwiththepurposeofaccuratelyandefficientlyestimat-XiaopingDu1ingthecumulativedistributionfunction(CDF),probabilitydensityfunction(PDF),andDr.statisticalmomentsofaresponsegiventhedistributionsofinputvariables.ThebivariateAssistantProfessordimensionreduction

4、methodandnumericalintegrationareusedtocalculatethemomentsDepartmentofMechanicalandAerospaceoftheresponse;thensaddlepointapproximationsareemployedtoestimatetheCDFandEngineering,PDFoftheresponse.Theproposedmethodrequiresneitherthederivativesofthere-UniversityofMis

5、souri–Rollasponsenorthesearchofthemostprobablepoint,whichisneededinthecommonlyusede-mail:dux@umr.edufirstandsecondorderreliabilitymethods(FORMandSORM)andtherecentlydevelopedfirstordersaddlepointapproximation.Theefficiencyandaccuracyoftheproposedmethodisillustratedw

6、iththreeexampleproblems.Withthesamecomputationalcost,thismethodismoreaccurateforreliabilityassessmentandmuchmoreefficientforestimatingthefullrangeofthedistributionofaresponsethanFORMandSORM.ThismethodprovidesresultsasaccurateasMonteCarlosimulation,withsignificantl

7、yreducedcom-putationaleffort.
DOI:10.1115/1.21186671IntroductionTraditionally,commonlyusedmethodscomprisethreemajorcategories:1analyticalmethods,2surrogatemethods,and3Thequantitativeassessmentoftheimpactoftheuncertaintyofsimulationmethods.Typicalanalytica

8、lmethodsincludethefirstinputvariablesonaresponseisnowwidelyrecognizedasanorderreliabilitymethodFORMandthesecondorderreliabilityimportantandindispensablecomponentinen